Stochastic resonance between dissipative structures in a bistable noise-sustained dynamics

Abstract

We study an extended system that without noise shows a monostable dynamics, but when submitted to an adequate multiplicative noise, an effective bistable dynamics arises. The stochastic resonance between the attractors of the noise-sustained dynamics is investigated theoretically in terms of a two-state approximation. The knowledge of the exact nonequilibrium potential allows us to obtain the output signal-to-noise ratio. Its maximum is predicted in the symmetric case for which both attractors have the same nonequilibrium potential value.

System size stochastic resonance: General nonequilibrium potential framework

“…In our previous work [15] we have found that the dependence of the SNR as a function of λ is maximum at the symmetric situation λ = λ c = 0.8, where both stable structures (φ 0 and φ s ) have the same stability (…”

“…The basic model to be considered in this section is the same one studied in [15], and consist of the following ensemble of nonlinear coupled oscillators, described in terms of a continuous field…”

“…(15) it is clear that U 0 ({x}), the potential function in Eqs. (15,16), is the discrete form of the NEP for this problem. For A = 0 the stationary distri-bution of the multidimensional Fokker-Planck equation associated to Eq.…”

“…Such a nonequilibrium potential, closely related to the solution of the time independent FokkerPlanck equation of the system, characterizes the global properties of the dynamics: that is attractors, relative (or nonlinear) stability of these attractors, height of the barriers separating attraction basins, and in addition it allows us to evaluate the transition rates among the different attractors [13,14]. In another recent paper we have explored the characteristics of this SR phenomenon in an extended system composed by an ensemble of noise-induced nonlinear oscillators coupled by a nonhomogeneous, density dependent diffusion, externally forced and perturbed by a multiplicative noise, that shows an effective noise induced bistable dynamics [15]. The stochastic resonance between the attractors of the noise-induced dynamics was theoretically investigated in terms of a two-state approximation.…”

“…Here, we discuss in more detail the cases analyzed in [21] and present a new interesting one, corresponding to the study of SSSR in a system that also shows noise induced patterns, the same one studied in [15]. We show that in two of the cases -corresponding to pattern forming systems that include only local interactions-the problem could be rewritten in such a way as to present a kind of "entrainment" between the symmetry breaking of an "effective" potential together with a scaling of the noise intensity with the system size.…”